Question: If infinitely many values of $y$ satisfy the equation $2(4+cy) = 12y+8$, then what is the value of $c$?
Answer: Simplifying both sides gives $8+2cy = 12y+8$.  Subtracting $8$ from both sides gives $2cy = 12y$.  If $c=\boxed{6}$, then this equation is always true, and the original equation is true for all $y$ (so it has infinitely many solutions).  Otherwise, the equation has only one solution ($y=0$).